Participants in the current study will receive daily injections of either pegvisomant or placebo (an inactive substance) for 12 weeks, followed by a 6-week "washout" period with no drug. Then, patients who received placebo will be switched, or "crossed over," to receive pegvisomant for another 12 weeks, and those who received pegvisomant will receive placebo. This will be followed by another 6-week washout period. The drug and placebo will be injected under the skin, similar to insulin injections. Blood and urine tests will be done at the beginning of the study and repeated every 6 weeks until the study ends.